Calculate My Home
Units

Stair Stringer Calculator

Enter the total rise and stair width to get the framing square settings, cut marks, throat depth, board length and stringer count.

Units
Stair for
Total rise
ft
in

Top of the decking down to the pad or grade, measured plumb.

in

Per step, nosing to nosing.

in

7 ¾ in max.

in

Drops the bottom of the stringer.

in
in

On center. Check your tread's span.

Framing square: tongue on the rise, body on the run

7 × 11 ¼in

Step it off 5 times for 6 risers. Cut 4 stringers from 8 ft 2×12s, and take 1 ½ in off the bottom so the first step matches the rest.
Throat
5 ⁵⁄₁₆ in
Stringer length
5 ft 5 ⁷⁄₁₆ in
Stringers
4at 16 in
Bottom drop
1 ½ in
Step on the board
13 ¼ in
Angle
31.9°
body 11 ¼ intongue 7 inthroat 5 ⁵⁄₁₆ in8 ft board, 5 ft 5 ⁷⁄₁₆ in used

Marks along the top edge

Measure from the square end of the board. At each mark, set the square's stair gauges at 7 in on the tongue and 11 ¼ in on the body, and trace the notch.

  1. Tread 12 ⅞ in
  2. Tread 21 ft 4 ⅛ in
  3. Tread 32 ft 5 ⅜ in
  4. Tread 43 ft 6 ⅝ in
  5. Tread 54 ft 7 ⅞ in

Stringer and code check

  • Throat 5 ⁵⁄₁₆ in

    5 in min, AWC DCA 6 Fig. 28

  • Riser height 7 in

    7 ¾ in max, IRC R311.7.5.1

  • Tread depth 11 ¼ in

    10 in min, IRC R311.7.5.2

  • Board 2×12

    2×12 min, AWC DCA 6

  • Stringer spacing 16 in

    18 in max, DCA 6 Fig. 29

  • Cut stringer span 4 ft 8 ¼ in

    6 ft max, DCA 6 Fig. 28

  • Total rise 3 ft 6 in

    12 ft max without a landing, DCA 6

The stair rises 3 ft 6 in: DCA 6 calls for a guard on the open sides from 30 in of total rise.

The math

  1. Risers

    42 in ÷ 7.5 in target, rounded (never above 7 ¾ in) = 6

  2. Riser (tongue)

    42 in ÷ 6 = 7 in

  3. Step on the board

    √(7 in² + 11.25 in²) = 13 ¼ in

  4. Throat

    11.25 in − (7 in × 11.25 in ÷ 13.25 in) = 5 ⁵⁄₁₆ in

  5. Total run

    5 treads × 11.25 in = 4 ft 8 ¼ in

  6. Stringer length

    outline measured along the board, level foot to plumb head cut = 5 ft 5 ⁷⁄₁₆ in

  7. Stringers

    (36 in − 1.5 in) ÷ 16 in, rounded up, + 1, at least 3 = 4

Material list

3 ft 6 in rise, 6 risers of 7 in, 5 treads of 11 ¼ in, 36 in wide.

QuantityItem
4pcs

2×12 pressure-treated or framing lumber, 8 ft

One stringer each, cut to 5 ft 5 ⁷⁄₁₆ in

10pcs

2×6 deck boards for treads

2 per tread, cut to 36 in

For a deck 3 ft 6 in (42 in) above the landing pad with 11¼ in treads, set the framing square at 7 in on the tongue and 11¼ in on the body and step it off five times. That gives 6 risers, 5 treads, 4 ft 8¼ in of run and a 5 ⁵⁄₁₆ in throat on a 2×12. Each stringer is 5 ft 5 ⁷⁄₁₆ in long, so an 8 ft board does it, and a 36 in wide stair takes 4 stringers at 16 in on center.

How the stringer layout is calculated

The stringer carries the same risers and treads the stair calculator works out: the total rise divided into equal risers of 7¾ in or less, with one tread fewer than risers. On the board, each step is a right triangle whose legs are the riser and the tread. Its long side lies along the top edge of the board, so each notch moves along the edge by that diagonal.

Step along the edge = √(riser² + tread²). Throat = board depth − (riser × tread ÷ step). Bottom drop = tread thickness.

For the default: √(7² + 11.25²) = 13.25 in per step along the edge. The deepest point of each notch sits 7 × 11.25 ÷ 13.25 = 5.94 in in from the edge, so an 11¼ in deep 2×12 keeps 11.25 − 5.94 = 5.31 in of solid wood under it, the throat.

Framing square settings

Clamp stair gauges (or a straight board) to the square with the riser on the narrow arm, the tongue, and the tread on the wide arm, the body. Lay the square on the board with both marks on the top edge and trace the notch. Slide it along until the tread mark meets the last riser line, and repeat. The marks table under the calculator gives each tread's corner measured from the square end of the board: for the default the first corner is 2 ⅞ in in, and each next one 13¼ in further.

At the bottom, the stringer sits on the pad with a level cut 12 ⁷⁄₁₆ in long. At the top, a plumb cut 6¼ in tall bears against the rim joist or hangs in sloped hangers.

Why the bottom of the stringer drops

Treads sit on top of the cuts, so every step gains the tread thickness, but the bottom step starts from the pad, not from a tread. Cut the thickness of one tread off the foot of the stringer: 1½ in for 2× deck boards, 1 in for 5/4 decking. Without the drop, the first riser comes out 1½ in taller than the rest and the last one 1½ in shorter, well past the ⅜ in variation IRC R311.7.5.1 allows between risers in a flight.

Throat depth: will a 2×12 do?

The American Wood Council's DCA 6 deck guide asks for 2×12 stringers with at least a 5 in throat, and its commentary says cut stringers were checked with 5.1 in of wood left at a 7¾ : 10 stair. Steep, deep steps eat the most wood:

Riser × treadThroat on a 2×12Throat on a 2×10
7¾ × 10 in5.12 in3.12 in
7½ × 10 in5.25 in3.25 in
7½ × 11 in5.05 in3.05 in
7 × 11 in5.34 in3.34 in
7¼ × 11¼ in5.16 in3.16 in
7¾ × 11¼ in4.87 in2.87 in
6½ × 12 in5.53 in3.53 in

A 2×10 never reaches 5 in at code stair sizes, which is why DCA 6 starts at 2×12. At 7¾ × 11¼ in even a 2×12 falls short: use one more riser, or a solid stringer with the treads on ledgers.

How many stringers for a stair

DCA 6 spaces cut stringers no more than 18 in on center under 2× or 5/4 wood treads, and asks for at least three. The calculator counts the spaces across the width and adds one:

Stair widthAt 16 in on centerAt 18 in on center
36 in43
48 in44
60 in55

Composite treads often need closer support; the tread maker's span for stairs decides.

Span, length and landings

A cut stringer in DCA 6 may span at most 6 ft horizontally before it needs a post under it or a landing; a solid stringer may run 13 ft 3 in. A deck stair taller than 12 ft needs an intermediate landing, which the stair landing calculator lays out. The stringer bottoms bear on a footing or on posts set below frost, not on an unfooted patio slab: size those with the deck footing calculator.

In metric, a 1.07 m rise with 28.5 cm treads and a 19 cm target gives 6 risers of 17.8 cm, a 13.5 cm throat and a 1.66 m stringer.

Next steps